Inverse multi-objective combinatorial optimization

Roland, Julien; Smet, Yves De; Figueira, José Rui

doi:10.1016/j.dam.2013.04.024

Cited by 15 publications

(5 citation statements)

References 47 publications

(93 reference statements)

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“…The inverse optimization research for DMP with multiobjective functions is rather new and much less investigated. Roland et al (2013) consider an IOP for a binary integer DMP given a set of linear objective functions, and develops branch-and-bound and cutting plane algorithms, which are not numerically evaluated yet, to find minimal adjustment of the objective functions such that a given set of feasible solutions becomes efficient. Research in Chan et al (2014) addresses another situation where preferences or weights of several known (linear) criteria in the decision making problem will be inferred based on a single noisy observation.…”

Section: Literature Reviewmentioning

confidence: 99%

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Inferring Parameters Through Inverse Multiobjective Optimization

Dong,

Zeng

2018

Preprint

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Given a set of human's decisions that are observed, inverse optimization has been developed and utilized to infer the underlying decision making problem. The majority of existing studies assumes that the decision making problem is with a single objective function, and attributes data divergence to noises, errors or bounded rationality, which, however, could lead to a corrupted inference when decisions are tradeoffs among multiple criteria. In this paper, we take a data-driven approach and design a more sophisticated inverse optimization formulation to explicitly infer parameters of a multiobjective decision making problem from noisy observations. This framework, together with our mathematical analyses and advanced algorithm developments, demonstrates a strong capacity in estimating critical parameters, decoupling "interpretable" components from noises or errors, deriving the denoised optimal decisions, and ensuring statistical significance. In particular, for the whole decision maker population, if suitable conditions hold, we will be able to understand the overall diversity and the distribution of their preferences over multiple criteria, which is important when a precise inference on every single decision maker is practically unnecessary or infeasible.Numerical results on a large number of experiments are reported to confirm the effectiveness of our unique inverse optimization model and the computational efficacy of the developed algorithms.

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Section: Literature Reviewmentioning

confidence: 99%

“…We note a couple of IOP studies have also investigated multiple objective function optimization (Roland et al 2013, Chan et al 2014. As pointed out in the following literature reviews, our research differs from them in model construction, computational methods, and statistical analysis and significance.…”

Section: Introductionmentioning

confidence: 99%

Inferring Parameters Through Inverse Multiobjective Optimization

Dong,

Zeng

2018

Preprint

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“…Inverse multiobjective optimization has focused on imputing the weights of subobjectives under different assumptions on Pareto optimality or feasibility of observations and availability of a prior weight vector (Roland et al., 2013; Chan et al., 2014; Chan and Lee, 2018; Naghavi et al., 2019; Ajayi et al., 2020; Dong and Zeng, 2020; Gebken and Peitz, 2021). If an attribute‐based forward problem can be reformulated as a multiobjective problem, then, under appropriate assumptions, the methods of inverse multiobjective optimization can be applied to solving IAO problems as well.…”

Section: Literature Reviewmentioning

confidence: 99%

Inverse attribute‐based optimization with an application in assortment optimization

H.Iraj

Terekhov

2022

Int Trans Operational Res

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Many applications of inverse optimization (IO) arise in settings where the goal is to predict the future actions of an optimizing agent (e.g., an optimizing customer's future purchases). The majority of papers in this area implicitly assume an alternative‐based modeling approach: The forward model finds an optimal set of actions (decisions) from among a given set of alternatives, while the inverse model imputes objective function coefficients corresponding to these alternatives. Since the imputed weights correspond only to alternatives existing in the training set, alternative‐based modeling is limited to applications where the set of options does not change when a prediction is needed. In this paper, we apply an attribute‐based perspective, which allows IO to impute the weights of attributes that lead to an optimal decision instead of imputing the weight of the decision itself. This perspective expands the range of IO applicability; we demonstrate that it facilitates the application of IO in assortment optimization, where changing product selections is a defining feature and accurate predictions of demand are important. We compare inverse attribute‐based optimization with rank‐based and machine learning methods. We show that since IO encodes the utility optimizing behavior of the consumer into the preference learning process, it results in lower assortment regret for the store and a lower utility gap for the consumers.

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“…Undoubtedly, new alternatives can be generated using other OR techniques such as inverse optimisation (e.g. [3], [78]) which allow dominated solutions (generally neglected), to become non-dominated with a minimal adjustment of the problem parameters (e.g. objective functions coefficients).…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Studying the generation of alternatives in public policy making processes

Ferretti

Pluchinotta

Tsoukiàs

2019

European Journal of Operational Research

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • This paper studies the alternatives' generation phase in policy making processes • We formalise the alternatives' construction process in two real projects • We discuss lessons learned on what generated novelty in these decision processes

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Inverse multi-objective combinatorial optimization

Cited by 15 publications

References 47 publications

Inferring Parameters Through Inverse Multiobjective Optimization

Inferring Parameters Through Inverse Multiobjective Optimization

Inverse attribute‐based optimization with an application in assortment optimization

Studying the generation of alternatives in public policy making processes

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